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That depends on that is in your set. ( However, 1/3 is always less than 1/2. )

Q: When is 1 half set less than 1 third set?

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The median, by definition, tells you the "half way point" of your data. Exactly half of the observations in the dataset will be less than the median and half will be greater than the median.

is a set of even numbers less than 8

Set of even numbers less than 50 and more than 40 = {42,44,46,48}

less than * * * * * Not quite - it does not say whether the minimum is "less than" something or something is "less than" the minimum! The minimum of a finite set of numbers is the smallest value in the set. It is a member of the set which is less than (or equal to) all members of the set. If you want a bit more, read on, otherwise the above will be fine. For an infinite set it is the largest number, which may or may not belong to the set, which is less than or equal to all members of the set. Why the distinction? Think of the set of positive integers. What is the minimum? Easy, it is 1. It is a member of the set and is less than or equal to all members of the set. So far so good. Now think of all positive fractions. The minimum? It is 0, but that is not a member of the set. On the other hand, no number bigger than 0 can be the minimum, because half that number will be a positive fraction but will be smaller than the minimum - ooops! Sometimes the minimum will be a member of the set, sometimes not - it depends on how the set is defined. Actually, the definition of the minimum is very, very important, because it forms the basis of Richard Dedekind's definition of numbers and all of number theory follows from it.

an empty set

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the median is a value of which half of all the values are less than, and half of all the values are greater than.

No. Not if 25% of the data set are all at the maximum value.

The median, by definition, tells you the "half way point" of your data. Exactly half of the observations in the dataset will be less than the median and half will be greater than the median.

The median is the middle number of any given set when they are in order, least to greatest. If there is an even number of values, the median is the average of the middle two. It tells you that half the members of the set are greater than it and half are less than it.

is a set of even numbers less than 8

the set of whole numbers less than 0

Set of even numbers less than 50 and more than 40 = {42,44,46,48}

The set of natural numbers less than four is {1, 2, 3}.

less than * * * * * Not quite - it does not say whether the minimum is "less than" something or something is "less than" the minimum! The minimum of a finite set of numbers is the smallest value in the set. It is a member of the set which is less than (or equal to) all members of the set. If you want a bit more, read on, otherwise the above will be fine. For an infinite set it is the largest number, which may or may not belong to the set, which is less than or equal to all members of the set. Why the distinction? Think of the set of positive integers. What is the minimum? Easy, it is 1. It is a member of the set and is less than or equal to all members of the set. So far so good. Now think of all positive fractions. The minimum? It is 0, but that is not a member of the set. On the other hand, no number bigger than 0 can be the minimum, because half that number will be a positive fraction but will be smaller than the minimum - ooops! Sometimes the minimum will be a member of the set, sometimes not - it depends on how the set is defined. Actually, the definition of the minimum is very, very important, because it forms the basis of Richard Dedekind's definition of numbers and all of number theory follows from it.

The set of positive integers less than 50 is finite (there are 49).The set of all integers less than 50 is infinite, because it includes an infinite number of negative numbers.

The set of positive odd integers.

an empty set